INTRODUCTION
Ultrasonic velocity of sound waves in a medium is fundamentally related to
the binding forces between the molecules. Ultrasonic velocities of the liquid
mixtures consisting of polar and nonpolar (Mehra and Pancholi,
2007) components are of considerable importance in understanding intermolecular
interaction between component molecules and find applications in several industrial
and technological processes (Pal and Kumar, 2004; Rao
et al., 2005). Ultrasonic velocity measurements have been employed
extensively to detect and assess weak and strong molecular interactions in binary
mixtures, because mixed solvents find practical applications in many chemical
and industrial processes. Increasing use of benzene and acetophenone in many
industrial processes have greatly stimulated the need for extensive information
on the acoustic and transport properties of these liquids and their mixtures.
The parameters such as ultrasonic velocity (u), density (ρ) and derived
parameters such as internal pressure (π_{i}), free volume (V_{f})
viscous relaxation time (τ) provide better insight into intermolecular
interactions. The investigation is carried out to study of molecular interactions
in the binary liquid mixtures of acetophenonebenzene. Several researchers (Savaroglu
and Aral, 2004; Sundharam and Palaniappan, 2005)
carried out ultrasonic investigations on liquid mixtures and correlated the
experimental results of ultrasonic velocity with the theoretical relations of
Nomoto, Vandeal and Vangeel and Rao’s specific velocity and interpreted
the results in terms of molecular interactions. The sound velocity in binary
liquid mixtures from various theoretical models has been compared in the present
paper. An attempt has been made to compare the merits of the existing relations
in binary liquid mixtures. The ultrasonic velocities of the binary liquid mixtures
of acetophenone and benzene at 303.15, 313.15 and 323.15 K over the entire range
have been theoretically evaluated by using various theories and compared with
experimental values.
MATERIALS AND METHODS
The chemicals used were of analytical reagent grade obtained from loba chemicals.
All the components were dried over anhydrous calcium chloride and fractionally
distilled (Oswal and Patel, 1995). Binary solutions
were prepared on percentage basis (v/v) by dissolving known volume of acetophenone
in appropriate volume of benzene and measuring their masses on a Shimadzu Corporation
Japan Type BL 2205 electronic balance accurate to 0.01 g. The possible uncertainty
in the mole fraction was estimated to be less than ±0.0001.The densities
were determined by using bicapillary pycnometer as described (MehdihasanUjjan
et al., 1995) and calibrated with deionised double distilled water
with 0.9960x10^{3} kg m^{3} as its density at temperature 303
K. The pycnometer filled with air bubble free experimental liquids was kept
in a transparent walled water bath to attain thermal equilibrium. The positions
of the liquid level in the two arms were recorded with a help of travelling
microscope which could read to 0.01 mm. The precision density measurements were
within ±0.0003 g cm^{3}. Speed of sound was measured by using
a variable path, single crystal interferometer (Mittal Enterprises, New Delhi).
The interferometer was calibrated using toluene. The interferometer cell was
filled with the test liquid and water was circulated around the measuring cell
from a thermostat. The uncertainty was estimated to be 0.1 m sec^{1}.
All measurements were made in a thermostatically controlled water bath with
temperature accuracy of ±0.1°C.
Theory: Using experimentally measured values of ultrasonic velocity
(u) and density (ρ) the following acoustic and thermodynamic parameters
are evaluated (Subha et al., 2004; Riggio
et al., 1986; Mehra and Pancholi, 2007; Mehra
et al., 2001). The internal pressure for pure liquids and their binary
liquid mixtures are calculated using the suryanarayana relation as given as:
where, b stands for cubic packing which is assumed to be 2 for liquids, K is dimensionless constant which is independent of temperature and nature of liquids and its value is 4.28x10^{9}, R is gas constant, T is absolute temperature and M_{eff} is effective molecular weight M_{eff} = X_{1}M_{1} + X_{2}M_{2}
Excess Gibb’s free energy of activation of viscous flow for binary liquid mixtures are obtained by using following expression:
The volume fraction of pure components Φi, was calculated from the individual pure molar volumes (Vi), with the relationship:
On assuming additivity of molar sound velocity Nomoto (1958)
established the following equation for sound velocity:
where, xi is the molefraction, Ri = u_{i}V_{i}^{1/3} the sound velocity, Vi the molar volume and u_{i} is the sound velocity of the ith component. Junjie’s equation is given by:
Rao’s (specific sound velocity) relation (Gokhale and Bhagavat, 1989) is given by:
where, r_{i}= u_{i}^{1/3}/ρi is the Rao’s specific sound velocity of the i^{th} component of the mixture.
RESULTS AND DISCUSSION
Table 1 summarizes the comparison of density (ρ) and ultrasonic velocity (u) data for pure liquids (acetophenone and benzene) at 303.15 K with the literature. The calculated quantities of internal pressure (π_{i}), excess gibbs energy (G^{E}), free volume (V_{f}) and viscous relaxation time (τ) of acetophenone and benzene system over the entire composition range at 303.15 K, 313.15 K and 323.15 K have been presented in Table 2.
Excess internal pressure (π_{i}^{E}), excess velocity (U^{E}) and excess free volume (V_{f}^{E}) were calculated from the experimental results by the following equations, respectively:
where, X_{1} and X_{2} are mole fractions, π_{i1 }and π_{i2 }are the internal pressures, U_{1} and U_{2} are the velocities and V_{f1} and
Table 1: 
Comparison of experimental density and sound of velocity of
pure liquids with literature values at 303.15 K 

Table 2: 
Experimental parameters (ρ, u), derived parameters (internal
pressure, Gibb’s free energy, free volume, relaxation time) for acetophenone
+ benzene system at 303.15, 313.15 and 323.15 K 

V_{f2} are the free volumes of component 1 and 2 respectively. The subscript M represents mixture properties. The variations of π_{i}^{E}, U^{E}, G^{E} and V_{f}^{E} with the molefraction of acetophenone at 303.15, 313.15 and 323.15 K are presented in Fig. 14.
The excess values of thermo physical properties and thermo acoustical parameters
of binary liquid mixtures are fitted to a RedlichKister (Redlich
and Kister, 1948) equation of the type:
where, Y represents excess internal pressure, excess free volume the corresponding equation. Coefficients Ai were obtained by fitting equation to experimental values using a least square regression method. In each case, the optimum number of coefficients is ascertained from an examination of the variation in standard deviation (S). S was calculated using the relation:

Fig. 1: 
Excess Gibb’s energy of activation of flow for acetophenone
(1) + benzene (2) at different temperatures 
where, N represents the number of experimental data points and n is the number of coefficients. It is found that for the solution of the seventh degree polynomial, the agreement between the experimental values and the calculated values is satisfactory. The coefficients and standard deviations of RedlichKister polynomial equation are presented in Table 3.
Table 3: 
RedlichKister constants for excess internal pressure and
excess Gibb’s free energy of Acetophenone  benzene at 303.15, 313.15
and 323.15 K 


Fig. 2: 
Excess Velocity for acetophenone (1) + benzene (2) at different
temperatures 

Fig. 3: 
Deviation of internal pressure for acetophenone (1) + benzene
(2) at different temperatures 
The excess Gibb’s free energy of activation of viscous flow, ΔG*^{E} is positive over the entire mole fraction range for the binary mixtures at different temperatures in Fig. 1. The sign of the values of ΔG*^{E} can be considered as a reliable criterion for detecting or excluding the presence of interaction between unlike molecules. The positive ΔG*^{E} values are also indicative of the strong molecular interaction between acetophenone and benzene. A detailed observation shows that the deviations of ultrasonic velocity of a mixture show increasing trend when mole fraction and temperature increases. It may be noted that such values are due to the electronic perturbation of the individual molecules during mixing and therefore depend very much on the nature of the mixing molecules. The internal pressure deviations are negative over the entire composition range of mixtures.

Fig. 4: 
Excess free volume for acetophenone (1) + benzene (2) at different
temperatures 
The excess free volumes are negative over the entire composition range of mixtures(Fort
and Moore, 1965; Mehra et al., 2001). This
suggests that the component molecules are closer together in the liquid mixture
than in the pure liquids forming the mixture, indicating that strong attractive
interactions between component molecules such as hydrogen bonding, dipoledipole
interactions and other specific interactions between unlike molecules are operative
in the system.
The experimental and theoretical velocities calculated by using the Eq.
68 are presented in Table 4. The validity
of different theoretical formulae is checked by percentage deviation for all
the mixtures at all the temperatures and is given in Table 4.
The limitations and approximation incorporated in these theories are responsible
for the deviations of theoretical from experimental values. In Nomoto’s
theory, no interaction between components of liquid mixtures has been taken
into account as it is supposed that the volume does not change on mixing. Similarly
the assumption for the formation of ideal mixing relation is that, the ratios
of specific heats of ideal mixtures and the volumes are equal by not taking
into the consideration of molecular interactions. Various types of forces such
as dispersion forces, charge transfer, hydrogen bonding, dipoledipole and dipoleinduced
dipole interactions are operative due to interactions when two liquids are mixed.
This is in good agreement with the conclusions drawn by
Padey et al. (1999) Thus the observed deviation of theoretical values
of velocity from the experimental values shows that the molecular interactions
is taking place between the unlike molecules in the liquid mixture.
Table 4: 
Values of ultrasonic velocity calculated from Nomoto, Junjie’s
and Rao’s relations along with experimental ultrasonic velocity and
percentage error for acetophenone +benzene at 303.15, 313.15 and 323.15
K 

There is a good agreement between experimental and theoretical values in Nomoto’s
relation followed by Rao’s specific velocity method whereas higher deviations
are observed in Junjie’s relations at all the temperatures.
CONCLUSION
Experimental data of the density and speed of sound of acetophenone and benzene mixtures have been measured over the entire composition range at 303.15, 313.15 and 323.15 k. it has been observed that positive deviations for excess velocity, excess internal pressure, excess Gibbs energy where as negative deviations were observed for excess free volume at 303.15, 313.15 and 323.15 k. The observed deviation of theoretical values of velocity from the experimental values is attributed to the presence of intermolecular interactions in the systems studied. It may be concluded that out of three theories and relations, Nomoto’s relation is best suited for the binary mixture of acetophenone +benzene at 303.15, 313.15 and 323.15 k.